SAN JUAN, Puerto Rico — Puerto Ricans are facing a fundamental question on their ballots: Should they change their ties with the United States?

Election Day is a holiday in the US island territory and the streets are quiet except around polling stations. The US island territory does not get a vote in the US presidential election.

But many are excited for a chance to vote in a referendum that asks voters if they want to change the relationship to the United States. A second question gives voters three alternatives: become the 51st US state, independence, or “sovereign free association,” a designation that would give more autonomy for the territory of 4 million people.

The island also is electing a governor.

Some polling stations opened late on Monday but the vote was otherwise orderly.